Question: The grades on a physics midterm at Covington are normally distributed with $\mu = 74$ and $\sigma = 2.5$. Tiffany earned a $67$ on the exam. Find the z-score for Tiffany's exam grade. Round to two decimal places.
Answer: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Tiffany's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{67 - {74}}{{2.5}}} $ ${ z \approx -2.80}$ The z-score is $-2.80$. In other words, Tiffany's score was $2.80$ standard deviations below the mean.